RIsk contribution

[shanlane]

Hello,

In the notes (and video) you state that if there is no correlation between assets then the addition of that asset will lead to zero risk contribution. I do not think this is correct, at least from a simple mathematical standpoint. UL(1)=30 and UL(2)=40. UL port if rho=0 is sqrt (900+1600)=sqrt(2500)=50. Both components still have risk contributions even though they have zero correlation.

Maybe there is a terminology mistake somewhere. Maybe you meant that the idiosyncratic UL is zero if rho=0? Not 100% sure about that either, but the idea sounds right.

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon

Yes, great observation and totally my mistake. As you example demonstrates or, if you enter zero (0) into default correlation in http://www.bionicturtle.com/how-to/spreadsheet/2011.t6.d.2.-ong-porfolio-ul , you will still get positive risk contributions.

It's based on my sloppy mis-read of the formula:

Sort of looks like rho(i,j) of zero will render numerator of zero...understandable, yes?
And the notes say, which looks mathematically correct: "At other extreme, if pairwise correlations are zero (0%), risk contribution equals zero."

But ... not really! the summation includes a term for the exposure's own unexpected loss, UL(i), so even if all the pair-wise correlations are zero, there is a term UL(i)*rho(i,i) = UL(i) since the correlation of the exposure with itself is 1.0; i.e., the diagonal of a correlation matrix is 1.0s ... i forgot to include the diagonal of 1.0s that informs the correlation matrix: all things have a 1.0 correlation with themselves.

So, thank you for noticing. My mistake, we will amend the notes to correct. Thanks,